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Mirrors > Home > MPE Home > Th. List > imp5g | Structured version Visualization version GIF version |
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.) |
Ref | Expression |
---|---|
imp5.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Ref | Expression |
---|---|
imp5g | ⊢ ((𝜑 ∧ 𝜓) → (((𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜂)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp5.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | 1 | imp4b 422 | . 2 ⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → (𝜏 → 𝜂))) |
3 | 2 | impd 411 | 1 ⊢ ((𝜑 ∧ 𝜓) → (((𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜂)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 |
This theorem is referenced by: (None) |
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